Is there a variant where life points are pooled with other players (3 players)?

[Rich Hutnik]

I was playing a 3 player version of Magic awhile back, where I felt
that two other players were making it a point to gang up and eliminate
me. To counter this double teaming, I thought of a variant.

In the variant, preferable for 3 players, whenever you attack one of
the two other players, damage is done to a common life pool shared
among them (players are partners with both players in a sense). So,
one player attacking a player would reduce one life pool, while
another player attacking the same player would reduce a different life
pool.

I was wondering if this variant exists. It is a bit like two-headed
giant, but might be thought of as three-headed giant in one sense.

Thanks...
- Rich